The ability to resolve all processes which drive galaxy formation is one of the most fundamental goals in extragalactic astronomy. While star formation rates and the merger history are now measured with increasingly high certainty, the role of gas accretion from the intergalactic medium in supplying gas for star formation still remains largely unknown. We present in this paper indirect evidence for the accretion of gas into massive galaxies with initial stellar masses M_*>10^{11} M_sol and following the same merger adjusted co-moving number density at lower redshifts during the epoch 1.5 < z < 3, using results from the GOODS NICMOS Survey (GNS). We show that the measured gas mass fractions of these massive galaxies are inconsistent with the observed star formation history for the same galaxy population. We further demonstrate that this additional gas mass cannot be accounted for by cold gas delivered through minor and major mergers. We also consider the effects of gas outflows and gas recycling due to stellar evolution in these calculations. We argue that to sustain star formation at the observed rates there must be additional methods for increasing the cold gas mass, and that the likeliest method for establishing this supply of gas is by accretion from the intergalactic medium. We calculate that the average gas mass accretion rate into these massive galaxies between 1.5 < z < 3.0, is \dot{M} = 96+/-19 M_sol/yr after accounting for outflowing gas. We show that during this epoch, and for these very massive galaxies, 49+/-20% of baryonic mass assembly is a result of gas accretion and unresolved mergers. However, 66+/-20% of all star formation in this epoch is the result of gas accretion. This reveals that for the most massive galaxies at 1.5< z< 3 gas accretion is the dominant method for instigating new stellar mass assembly.
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